The secret ingredient is something called polydiallyldimethylammonium chloride, AKA polyDADMAC, AKA polyDDA, AKA polyquaternium-6. The name sounds scary but the chemical itself is harmless. It is what is called a homopolymer and is used extensively in wastewater treatment.
PolyDADMAC works as a "flocculation agent", which is a process in which colloids (fish waste) come out of suspension in the form of flakes or floc
PolyDADMAC is so effective that a mere 200 grams can treat about 1 ton of wastewater. This is why just a few drops cleans up cloudy aquariums so well.
As many hobbyists already know, there are many similarities between aquarium filtration techniques and municipal wastewater treatment. In many ways keeping an aquarium environment healthy and stable is more challenging than treating Super Bowl half-time flushes.